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5 Changes from Earlier Versions
5.1 Changes between GAP 4.3 and GAP 4.4
5.1-1 Potentially Incompatible Changes
5.1-2 New Packages
5.1-3 Performance Enhancements
5.1-4 New Programming and User Features
5.2 Earlier Changes

### 5 Changes from Earlier Versions

#### 5.1 Changes between GAP 4.3 and GAP 4.4

The main changes between GAP 4.3 and GAP 4.4 are:

##### 5.1-1 Potentially Incompatible Changes

- The mechanism for the loading of Packages has changed to allow easier updates independent of main GAP releases. Packages require a file `PackageInfo.g` now. The new `PackageInfo.g` files are available for all packages with the new version of GAP (see Example: PackageInfo.g for a GAP package).

- `IsSimpleGroup` (Reference: IsSimpleGroup) returns false now for the trivial group.

- `PrimeBlocks` (Reference: PrimeBlocks): The output format has changed.

- Division rings (see `IsDivisionRing` (Reference: IsDivisionRing)) are now implemented as `IsRingWithOne` (Reference: IsRingWithOne).

- `DirectSumOfAlgebras` (Reference: DirectSumOfAlgebras (for two algebras)): \(p\)-th power maps are compatible with the input now.

- The print order for polynomials has been changed.

These changes are, in some respects, departures from our policy of maintaining upward compatibility of documented functions between releases. In the first case, we felt that the old behavior was sufficiently inconsistent, illogical, and impossible to document that we had no alternative but to change it. In the case of the package interface, the change was necessary to introduce new functionality. The planned and phased removal of a few unnecessary functions or synonyms is needed to avoid becoming buried in "legacy" interfaces, but we remain committed to our policy of maintaining upward compatibility whenever sensibly possible.

- Groebner Bases:

  Buchberger's algorithm to compute Groebner Bases has been implemented in GAP. (A. Hulpke)

- For large scale Groebner Basis computations there also is an interface to the Singular system available in the Singular package. (M. Costantini and W. de Graaf)

- New methods for factorizing polynomials over algebraic extensions of the rationals have been implemented in GAP. (A. Hulpke)

- For more functionality to compute with algebraic number fields there is an interface to the Kant system available in the Alnuth package. (B. Assmann and B. Eick)

- A new functionality to compute the minimal normal subgroups of a finite group, as well as its socle, has been installed. (B. Höfling)

- A fast method for recognizing whether a permutation group is symmetric or alternating is available now (A. Seress)

- A method for computing the Galois group of a rational polynomial is available again. (A. Hulpke)

- The algorithm for `BrauerCharacterValue` (Reference: BrauerCharacterValue) has been extended to the case where the splitting field is not supported in GAP. (T. Breuer)

- Brauer tables of direct products can now be constructed from the known Brauer tables of the direct factors. (T. Breuer)

- Basic support for vector spaces of rational functions and of uea elements is available now in GAP. (T. Breuer and W. de Graaf)

- Various new functions for computations with integer matrices are available, such as methods for computing normal forms of integer matrices as well as nullspaces or solutions systems of equations. (W. Nickel and F. Gähler)

##### 5.1-2 New Packages

The following new Packages have been accepted.

- Alnuth: Algebraic Number Theory and an interface to the Kant system. By B. Assmann and B. Eick.

- LAGUNA: Computing with Lie Algebras and Units of Group Algebras. By V. Bovdi, A. Konovalov, R. Rossmanith, C. Schneider.

- NQ: The ANU Nilpotent Quotient Algorithm. By W. Nickel.

- KBMAG: Knuth-Bendix for Monoids and Groups. By D. Holt.

- Polycyclic: Computation with polycyclic groups. By B. Eick and W. Nickel.

- QuaGroup: Computing with Quantized Enveloping Algebras. By W. de Graaf.

##### 5.1-3 Performance Enhancements

- The computation of irreducible representations and irreducible characters using the Baum-Clausen algorithm and the implementation of the Dixon-Schneider algorithm have been speeded up.

- The algorithm for `PossibleClassFusions` (Reference: PossibleClassFusions) has been changed: the efficiency is improved and a new criterion is used. The algorithm for `PossibleFusionsCharTableTom` (Reference: PossibleFusionsCharTableTom) has been speeded up. The method for `PrimeBlocks` (Reference: PrimeBlocks) has been improved following a suggestion of H. Pahlings.

- New improved methods for normalizer and subgroup conjugation in \(S_n\) have been installed and new improved methods for `IsNaturalSymmetricGroup` (Reference: IsNaturalSymmetricGroup) and `IsNaturalAlternatingGroup` (Reference: IsNaturalAlternatingGroup) have been implemented. These improve the available methods when groups of large degrees are given.

- The partition split method used in the permutation backtrack is now in the kernel. Transversal computations in large permutation groups are improved. Homomorphisms from free groups into permutation groups now give substantially shorter words for preimages.

- The membership test in `SP` (Reference: Sp (for dimension and field size)) and `SU` (Reference: SU) groups has been improved using the invariant forms underlying these groups.

- An improvement for the cyclic extension method for the computation of subgroup lattices has been implemented.

- A better method for `MinimalPolynomial` (Reference: MinimalPolynomial) for finite field matrices has been implemented.

- The display has changed and the arithmetic of multivariate polynomials has been improved.

- The `LogMod` (Reference: LogMod) function now uses Pollard's rho method combined with the Pohlig/Hellmann approach.

- Various functions for sets and lists have been improved following suggestions of L. Teirlinck. These include: `Sort` (Reference: Sort), `Sortex` (Reference: Sortex), `SortParallel` (Reference: SortParallel), `SortingPerm` (Reference: SortingPerm), `NrArrangements` (Reference: NrArrangements).

- The methods for `StructureConstantsTable` (Reference: StructureConstantsTable) and `GapInputSCTable` (Reference: GapInputSCTable) have been improved in the case of a known (anti-) symmetry following a suggestion of M. Costantini.

The improvements listed in this Section have been implemented by T. Breuer and A. Hulpke.

##### 5.1-4 New Programming and User Features

- The 2GB limit for workspace size has been removed and version numbers for saved workspaces have been introduced. (S. Linton and B. Höfling)

- The limit on the total number of types created in a session has been removed. (S. Linton)

- There is a new mechanism for loading packages available. Packages need a file `PackageInfo.g` now. (T. Breuer and F. Lübeck; see Example: PackageInfo.g for a GAP package).

Finally, as always, a number of bugs have been fixed. This release thus incorporates the contents of all the bug fixes which were released for GAP 4.3. It also fixes a number of bugs discovered since the last bug fix.

#### 5.2 Earlier Changes

The most important changes between GAP 4.2 and GAP 4.3 were:

- The performance of several routines has been substantially improved.

- The functionality in the areas of finitely presented groups, Schur covers and the calculation of representations has been extended.

- The data libraries of transitive groups, finite integral matrix groups, character tables and tables of marks have been extended.

- The Windows installation has been simplified for the case where you are installing GAP in its standard location.

- Many bugs have been fixed.

The most important changes between GAP 4.1 and GAP 4.2 were:

- A much extended and improved library of small groups as well as associated `IdGroup` (Reference: IdGroup) routines.

- The primitive groups library has been made more independent of the rest of GAP, some errors were corrected.

- New (and often much faster) infrastructure for orbit computation, based on a general "dictionary" abstraction.

- New functionality for dealing with representations of algebras, and in particular for semisimple Lie algebras.

- New functionality for binary relations on arbitrary sets, magmas and semigroups.

- Bidirectional streams, allowing an external process to be started and then controlled "interactively" by GAP

- A prototype implementation of algorithms using general subgroup chains.

- Changes in the behavior of vectors over small finite fields.

- A fifth book "New features for Developers" has been added to the GAP manual.

- Numerous bug fixes and performance improvements

The changes between the final release of GAP 3 (version 3.4.4) and GAP 4 are wide-ranging. The general philosophy of the changes is two-fold. Firstly, many assumptions in the design of GAP 3 revealed its authors' primary interest in group theory, and indeed in finite group theory. Although much of the GAP 4 library is concerned with groups, the basic design now allows extension to other algebraic structures, as witnessed by the inclusion of substantial bodies of algorithms for computation with semigroups and Lie algebras. Secondly, as the scale of the system, and the number of people using and contributing to it has grown, some aspects of the underlying system have proved to be restricting, and these have been improved as part of comprehensive re-engineering of the system. This has included the new method selection system, which underpins the library, and a new, much more flexible, GAP package interface.

Details of these changes can be found in the document "Migrating to GAP 4" available at the GAP website, see http://www.gap-system.org/Gap3/migratedoc.pdf.

It is perhaps worth mentioning a few points here.

Firstly, much remains unchanged, from the perspective of the mathematical user:

- The syntax of that part of the GAP language that most users need for investigating mathematical problems.

- The great majority of function names.

- Data libraries and the access to them.

A number of visible aspects have changed:

- Some function names that need finer specifications now that there are more structures available in GAP.

- The access to information already obtained about a mathematical structure. In GAP 3 such information about a group could be looked up by directly inspecting the group record, whereas in GAP 4 functions must be used to access such information.

Behind the scenes, much has changed:

- A new kernel, with improvements in memory management and in the language interpreter, as well as new features such as saving of workspaces and the possibility of compilation of GAP code into C.

- A new structure to the library, based upon a new type and method selection system, which is able to support a broader range of algebraic computation and to make the structure of the library simpler and more modular.

- New and faster algorithms in many mathematical areas.

- Data structures and algorithms for new mathematical objects, such as algebras and semigroups.

- A new and more flexible structure for the GAP installation and documentation, which means, for example, that a GAP package and its documentation can be installed and be fully usable without any changes to the GAP system.

Very few features of GAP 3 are not yet available in GAP 4.

- Not all of the GAP 3 packages have yet been converted for use with GAP 4.

- The library of crystallographic groups which was present in GAP 3 is now part of a GAP 4 package CrystCat by V. Felsch and F. Gähler.

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